https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=7h3.D3m0n.117&feedformat=atomAoPS Wiki - User contributions [en]2022-01-23T18:56:38ZUser contributionsMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=Shoelace_Theorem&diff=28221Shoelace Theorem2008-10-19T13:21:47Z<p>7h3.D3m0n.117: /* Theorem */</p>
<hr />
<div>The '''Shoelace Theorem''' is a nifty formula for finding the [[area]] of a [[polygon]] given the [[Cartesian coordinate system | coordinates]] of its [[vertex|vertices]].<br />
<br />
==Theorem==<br />
Suppose the polygon <math>P</math> has vertices <math>(a_1, b_1)</math>, <math>(a_2, b_2)</math>, ... , <math>(a_n, b_n)</math>, listed in clockwise order. Then area of <math>P</math> is<br />
<br />
<cmath>\dfrac{1}{2} |(a_1b_2 + a_2b_3 + \cdots + a_nb_1) - (b_1a_2 + b_2a_3 + \cdots + b_na_1)|</cmath><br />
<br />
The Shoelace Theorem gets its name because if one lists the the coordinates in a column,<br />
<cmath>\begin{align*}<br />
(a_1 &, b_1) \\<br />
(a_2 &, b_2) \\<br />
& \vdots \\<br />
(a_n &, b_n) \\<br />
(a_1 &, b_1)<br />
\end{align*},</cmath><br />
and marks the pairs of coordinates to be multiplied, the resulting image looks like laced-up shoes.<br />
<br />
==Proof==<br />
{{incomplete|proof}}<br />
<br />
{{stub}}<br />
<br />
[[Category:Geometry]]<br />
[[Category:Theorems]]</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=Equation&diff=24828Equation2008-04-16T22:23:26Z<p>7h3.D3m0n.117: </p>
<hr />
<div>{{stub}}<br />
{{WotWAnnounce|week=April 15-22}}<br />
An '''equation''' is a [[relation]] which states that two [[expression]]s are equal, identical, or otherwise the same. Equations are easily identifiable because they are composed of two expressions with an equals sign ('=') between them. <br />
<br />
Equations are similar to [[congruence]]s (which relate geometric figures instead of numbers) and other relationships which fall into the category of [[equivalence relation]]s.<br />
<br />
A unique aspect to equations is the ability to modify an original equation by performing operations (such as addition, subtraction, multiplication, division, and powers). <br />
<br />
==See also==<br />
* [[Inequality]]</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=Mathematics&diff=23012Mathematics2008-02-05T22:11:34Z<p>7h3.D3m0n.117: </p>
<hr />
<div>{{WotWAnnounce|week=February 4-11}}<br />
'''Mathematics''' is the [[science]] of [[number]]s, and the study of relationships that exist between them.<br />
<br />
==Overview=={{asy image|<math>1\,2\,3\,4\,5\,6\,7\,8\,9\,0</math>|right|The ten [[digit]]s making up <br /> the base ten number system.}}<br />
Modern mathematics is normally built around [[base numbers|base 10]], with ten digits. (<math>0,1,2,3,4,5,6,7,8,9</math>) Modern mathematics is separated into two categories: discrete mathematics and non-discrete.<br />
===Non-Discrete Mathematics===<br />
Non-discrete mathematics is study of mathematics that is generally applicable to the "real world", such as [[algebra]], [[geometry|Euclidean geometry]], [[statistics]], and other such topics. (Note that the real world is actually only approximately Euclidean if one studies large areas of it, infinitesimal areas actually are non-Euclidean) There is some controversy over what varieties of algebra are non-discrete, but it is generally agreed that elementary and superior algebra are non-discrete, while [[abstract algebra]] and intermediate topics such as [[field theory|field]] and [[graph theory]] and [[Diophantine]] equations are discrete.<br />
<br />
===Discrete Mathematics===<br />
[[Combinatorics]], [[number theory]], and some of the algebraic fields mentioned above are examples of discrete mathematics. Topics of discrete mathematics are generally not directly applicable to the "real world", and if they are, it is only in an abstract fashion.<br />
==History of Mathematics==<br />
Mathematics was noted by the earliest humans. Over time, as humans evolved, the complexity of mathematics also evolved. There was an astounding discovery on how the numbers correlated with each other, as well as in nature, so well, as they created the concept of numbers. As a great 19th century thinker said,<br />
<br />
"God created the integers. All the rest is the work of man." (Leopold Kronecker)<br />
<br />
<br />
== See also ==<br />
* [[Math books]]<br />
* [[Mathematics competitions]]</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=Law_of_Sines&diff=22909Law of Sines2008-02-02T02:47:50Z<p>7h3.D3m0n.117: /* Theorem */</p>
<hr />
<div>The '''Law of Sines''' is a useful identity in a [[triangle]], which, along with the [[law of cosines]] and the [[law of tangents]] can be used to determine sides and angles. The law of sines can also be used to determine the [[circumradius]], another useful function.<br />
<br />
==Theorem==<br />
In triangle <math>\triangle ABC</math>, where <math>a</math> is the side opposite <math>A</math>, <math>b</math> opposite <math>B</math>, and <math>c</math> opposite <math>C</math>:<br />
<br />
<math>\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=2R</math><br />
<br />
==Proof ==<br />
=== Method 1 ===<br />
In the diagram below, circle <math> O </math> [[circumscribe]]s triangle <math> ABC </math>. <math> OD </math> is [[perpendicular]] to <math> BC </math>. Since <math> \triangle ODB \cong \triangle ODC </math>, <math> BD = CD = \frac a2 </math> and <math> \angle BOD = \angle COD </math>. But <math> \angle BAC = 2\angle BOC </math> making <math> \angle BOD = \angle COD = \theta </math>. Therefore, we can use simple trig in [[right triangle]] <math> BOD </math> to find that <br />
<br />
<center><math> \sin \theta = \frac{\frac a2}R \Leftrightarrow \frac a{\sin\theta} = 2R. </math> </center><br />
<br />
The same holds for <math>b</math> and <math>c</math>, thus establishing the identity.<br />
<br />
<center>[[Image:Lawofsines.PNG]] <br />
{{asy replace}}<br />
</center><br />
=== Method 2 ===<br />
This method only works to prove the regular (and not extended) Law of Sines.<br />
<br />
The formula for the area of a triangle is: <br />
<math>[ABC] = \frac{1}{2}ab\sin C </math><br />
<br />
Since it doesn't matter which sides are chosen as <math>a</math>, <math>b</math>, and <math>c</math>, the following equality holds: <br />
<br />
<math>\frac{1}{2}bc\sin A = \frac{1}{2}ac\sin B = \frac{1}{2}ab\sin C </math><br />
<br />
Multiplying the equation by <math>\frac{2}{abc} </math> yields: <br />
<br />
<math>\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c} </math><br />
<br />
==Problems==<br />
===Introductory===<br />
*If the sides of a triangle have lengths 2, 3, and 4, what is the radius of the circle circumscribing the triangle?<br />
<br />
<center><math><br />
\mathrm{(A) \ } 2<br />
\qquad \mathrm{(B) \ } 8/\sqrt{15} <br />
\qquad \mathrm{(C) \ } 5/2<br />
\qquad \mathrm{(D) \ } \sqrt{6}<br />
\qquad \mathrm{(E) \ } (\sqrt{6} + 1)/2<br />
</math></center><br />
<br />
([[University of South Carolina High School Math Contest/1993 Exam/Problem 29|Source]])<br />
===Intermediate===<br />
*[[Triangle]] <math>ABC</math> has sides <math>\overline{AB}</math>, <math>\overline{BC}</math>, and <math>\overline{CA}</math> of [[length]] 43, 13, and 48, respectively. Let <math>\omega</math> be the [[circle]] [[circumscribe]]d around <math>\triangle ABC</math> and let <math>D</math> be the [[intersection]] of <math>\omega</math> and the [[perpendicular bisector]] of <math>\overline{AC}</math> that is not on the same side of <math>\overline{AC}</math> as <math>B</math>. The length of <math>\overline{AD}</math> can be expressed as <math>m\sqrt{n}</math>, where <math>m</math> and <math>n</math> are [[positive integer]]s and <math>n</math> is not [[divisibility | divisible]] by the [[square]] of any [[prime]]. Find the greatest [[integer]] less than or equal to <math>m + \sqrt{n}</math>.<br />
<br />
([[Mock AIME 4 2006-2007 Problems/Problem 15|Source]])<br />
===Advanced===<br />
Let <math>ABCD </math> be a convex quadrilateral with <math>AB=BC=CD </math>, <math>AC \neqBD </math>, and let <math>E </math> be the intersection point of its diagonals. Prove that <math>AE=DE </math> if and only if <math> \angle BAD+\angle ADC = 120^{\circ} </math>.<br />
<br />
([[2007 BMO Problems/Problem 1|Source]])<br />
==See Also==<br />
* [[Trigonometry]]<br />
* [[Trigonometric identities]]<br />
* [[Geometry]]<br />
* [[Law of Cosines]]<br />
[[Category:Trigonometry]]</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=Law_of_Sines&diff=22908Law of Sines2008-02-02T02:47:26Z<p>7h3.D3m0n.117: /* Theorem */</p>
<hr />
<div>The '''Law of Sines''' is a useful identity in a [[triangle]], which, along with the [[law of cosines]] and the [[law of tangents]] can be used to determine sides and angles. The law of sines can also be used to determine the [[circumradius]], another useful function.<br />
<br />
==Theorem==<br />
In triangle <math>\triangle ABC</math>, where <math>a</math> is the side opposite <math>A</math>, <math>b</math> opposite <math>B</math>, <math>c</math> opposite <math>C</math>, and <math></math> is the circumradius:<br />
<br />
<math>\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}=2R</math><br />
<br />
==Proof ==<br />
=== Method 1 ===<br />
In the diagram below, circle <math> O </math> [[circumscribe]]s triangle <math> ABC </math>. <math> OD </math> is [[perpendicular]] to <math> BC </math>. Since <math> \triangle ODB \cong \triangle ODC </math>, <math> BD = CD = \frac a2 </math> and <math> \angle BOD = \angle COD </math>. But <math> \angle BAC = 2\angle BOC </math> making <math> \angle BOD = \angle COD = \theta </math>. Therefore, we can use simple trig in [[right triangle]] <math> BOD </math> to find that <br />
<br />
<center><math> \sin \theta = \frac{\frac a2}R \Leftrightarrow \frac a{\sin\theta} = 2R. </math> </center><br />
<br />
The same holds for <math>b</math> and <math>c</math>, thus establishing the identity.<br />
<br />
<center>[[Image:Lawofsines.PNG]] <br />
{{asy replace}}<br />
</center><br />
=== Method 2 ===<br />
This method only works to prove the regular (and not extended) Law of Sines.<br />
<br />
The formula for the area of a triangle is: <br />
<math>[ABC] = \frac{1}{2}ab\sin C </math><br />
<br />
Since it doesn't matter which sides are chosen as <math>a</math>, <math>b</math>, and <math>c</math>, the following equality holds: <br />
<br />
<math>\frac{1}{2}bc\sin A = \frac{1}{2}ac\sin B = \frac{1}{2}ab\sin C </math><br />
<br />
Multiplying the equation by <math>\frac{2}{abc} </math> yields: <br />
<br />
<math>\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c} </math><br />
<br />
==Problems==<br />
===Introductory===<br />
*If the sides of a triangle have lengths 2, 3, and 4, what is the radius of the circle circumscribing the triangle?<br />
<br />
<center><math><br />
\mathrm{(A) \ } 2<br />
\qquad \mathrm{(B) \ } 8/\sqrt{15} <br />
\qquad \mathrm{(C) \ } 5/2<br />
\qquad \mathrm{(D) \ } \sqrt{6}<br />
\qquad \mathrm{(E) \ } (\sqrt{6} + 1)/2<br />
</math></center><br />
<br />
([[University of South Carolina High School Math Contest/1993 Exam/Problem 29|Source]])<br />
===Intermediate===<br />
*[[Triangle]] <math>ABC</math> has sides <math>\overline{AB}</math>, <math>\overline{BC}</math>, and <math>\overline{CA}</math> of [[length]] 43, 13, and 48, respectively. Let <math>\omega</math> be the [[circle]] [[circumscribe]]d around <math>\triangle ABC</math> and let <math>D</math> be the [[intersection]] of <math>\omega</math> and the [[perpendicular bisector]] of <math>\overline{AC}</math> that is not on the same side of <math>\overline{AC}</math> as <math>B</math>. The length of <math>\overline{AD}</math> can be expressed as <math>m\sqrt{n}</math>, where <math>m</math> and <math>n</math> are [[positive integer]]s and <math>n</math> is not [[divisibility | divisible]] by the [[square]] of any [[prime]]. Find the greatest [[integer]] less than or equal to <math>m + \sqrt{n}</math>.<br />
<br />
([[Mock AIME 4 2006-2007 Problems/Problem 15|Source]])<br />
===Advanced===<br />
Let <math>ABCD </math> be a convex quadrilateral with <math>AB=BC=CD </math>, <math>AC \neqBD </math>, and let <math>E </math> be the intersection point of its diagonals. Prove that <math>AE=DE </math> if and only if <math> \angle BAD+\angle ADC = 120^{\circ} </math>.<br />
<br />
([[2007 BMO Problems/Problem 1|Source]])<br />
==See Also==<br />
* [[Trigonometry]]<br />
* [[Trigonometric identities]]<br />
* [[Geometry]]<br />
* [[Law of Cosines]]<br />
[[Category:Trigonometry]]</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:Chess/Chess_Tournament_Info/Round_1&diff=20427AoPS Wiki:Chess/Chess Tournament Info/Round 12007-12-01T15:11:32Z<p>7h3.D3m0n.117: /* Pairings */</p>
<hr />
<div>Round 1 will commence on December 7th!<br />
<br />
==Pairings==<br />
*Game 1: <b>Team Alpha</b> (White) vs. <b>Team Theta</b> (Black)<br />
<br />
*Game 2: <b>Team Beta</b> (White) vs. <b>Team Eta</b> (Black)<br />
<br />
*Game 3: <b>Team Gamma</b> (White) vs. <b>Team Zeta</b> (Black)<br />
<br />
*Game 4: <b>Team Delta</b> (White) vs. <b>Team Epsilon</b> (Black)<br />
<br />
==Games==<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 1/Game 1|Game 1]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 1/Game 2|Game 2]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 1/Game 3|Game 3]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 1/Game 4|Game 4]]<br />
<br />
{{chess round|r=Round 1|p=Round 1|n=Round 2}}<br />
[[Category:AoPSWiki Games]]<br />
[[Category:Current Round 1 Chess Games|*]]</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:Chess/Chess_Tournament_Info/Round_1&diff=20426AoPS Wiki:Chess/Chess Tournament Info/Round 12007-12-01T15:09:37Z<p>7h3.D3m0n.117: </p>
<hr />
<div>Round 1 will commence on December 7th!<br />
<br />
==Pairings==<br />
*Game 1: Team Alpha(White) vs. Team Theta (Black)<br />
<br />
*Game 2: Team Beta(White) vs. Team Eta(Black)<br />
<br />
*Game 3: Team Gamma(White) vs. Team Zeta(Black)<br />
<br />
*Game 4: Team Delta(White) vs. Team Epsilon(Black) <br />
<br />
==Games==<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 1/Game 1|Game 1]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 1/Game 2|Game 2]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 1/Game 3|Game 3]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 1/Game 4|Game 4]]<br />
<br />
{{chess round|r=Round 1|p=Round 1|n=Round 2}}<br />
[[Category:AoPSWiki Games]]<br />
[[Category:Current Round 1 Chess Games|*]]</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:Chess/Chess_Tournament_Info&diff=20070AoPS Wiki:Chess/Chess Tournament Info2007-11-24T14:49:07Z<p>7h3.D3m0n.117: /* Team Eta (<math>\eta</math>) */</p>
<hr />
<div>__NOTOC__<br />
<br />
:'''Update as of Saturday 11/24: SIGN UPS CLOSED! TOURNAMENT WILL BEGIN SOON!'''<br />
<br />
:'''Note: This article is more updated than the information in the topic; so if there are any discrepancies, then this probably has the correct information!'''<br />
<br />
:'''Note: i_like_pie seems to be currently inactive, so 7h3.D3m0n.117 is temporarily taking over as head TD. Any questions regarding the tournament can be pmed to either Temperal or 7h3.D3m0n.117.'''<br />
<br />
===Teams===<br />
Each team will consist of either 4 or 5 players. It is suggested only people who already know each other make teams of 5 people as it can be harder to communicate with more people. Players can agree between themselves and create their own teams. Others who haven't made their own teams will be randomized into teams.<br />
<br />
During the tournament, a team cannot request to have another player added to their team unless one of their players cannot participate anymore. Players cannot switch teams, so choose wisely if you pick your own teams.<br />
<br />
===Rules===<br />
A team must post a move within 2 days after the other team's move. Each time a team fails to do so (unless there is a good reason), a warning will be issued. 5 warnings will result in disqualification.<br />
<br />
The use of computers, chess programs, and other devices that give your team an advantage is not allowed. This rule cannot be strictly enforced, but hopefully people will play fairly as this tournament is for fun only.<br />
<br />
===Tournament Format===<br />
Depending on the amount of players and teams, there will be several rounds of Swiss, followed by single elimination for the final rounds. For the final game, 3 days will be allowed per move.<br />
<br />
===Signing Up===<br />
Before signing up, please make sure you will be able to participate. [[User:I like pie|I_like_pie]] will accept sign ups via post in the [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=164632 original topic], <url>privmsg.php?mode=post&u=22236 PM</url>, or email (nkouevda@gmail.com).<br />
<br />
Sign ups (as of November 24, 2007) are closed.<br />
<br />
===Playing===<br />
All games will be played on the Math and Strategy forum, with a representative from each team (the designated ''<span style="color:blue">Poster</span>'') posting moves when it is their team's turn. <br />
<br />
All games will be documented on the Wiki:<br />
<br />
Here is the format for the page name of each game: '''AoPSWiki:Chess/Chess Tournament Info/Round <nowiki>#</nowiki>/Game <nowiki>#</nowiki>''', where the first <nowiki>#</nowiki> is the round number and the second is the game number. All of these would be part of '''Category:Current Round # Chess Games'''.<br />
<br />
The format of the last two rounds will be different.<br />
<br />
'''AoPSWiki:Chess/Chess Tournament Info/Semifinals/Game #''': all of these would be part of '''Category:Current Semifinals Chess Games'''<br />
<br />
'''AoPSWiki:Chess/Chess Tournament Info/Finals/Game #''': all of these would be part of '''Category:Current Finals Chess Games'''<br />
===FAQ===<br />
====When will the pairings be up?====<br />
<br />
As mentioned above, pairings will be up in the next week.<br />
----<br />
====When do games start?====<br />
<br />
Games will start in the Math&Strat Forum exactly 7 days after pairings are posted. This allows team members to communicate, get to know each other, and plan their openings. Some people also might be on vacation so this extra week will allow the people to return. An estimated date? December 7.<br />
----<br />
====Do we play the games on Wiki or the Math and Strategy Forum?====<br />
<br />
We would ask you to play the games in the forum because it's easier to keep track of things and it could be confusing for posters on the Wiki. <br />
----<br />
====Will the Wiki game/round pages have any use?====<br />
<br />
Yes, Temperal will be documenting every move on the wiki with those pages to prevent cheating, illegal moves, etc.<br />
----<br />
====Will there be a standardized title for the topics?====<br />
<br />
The titles will be: "Chess tournament: Round x, Game y, Team a vs. Team b".<br />
----<br />
====How many rounds will this tournament be?====<br />
<br />
Four rounds of randomized Swiss, then the semi-finals and finals (referred to collectively as the playoffs), which are single elimination.<br />
----<br />
====Will there be appeals for rematches?====<br />
<br />
No. If you made a terrible mistake unrepresentative of your playing level, so be it. We're not extending this already-long tournament even more.<br />
----<br />
====When will each new round begin?====<br />
<br />
As soon as all games in the previous one are finished. If a game is taking *way* too long, it will be up to a TD's discretion to declare it a win, loss, or draw.<br />
<br />
===List of Players===<br />
35 Players:<br />
#[[User:I like pie|i_like_pie]]<br />
#[[User:7h3.D3m0n.117|7h3.D3m0n.117]]<br />
#cincodemayo5590<br />
#BoesFX<br />
#[[User:Temperal|Temperal]]<br />
#shaggy75<br />
#Tenoreoz<br />
#[[User:abacadaea|abacadaea]]<br />
#[[User:nayel|nayel]]<br />
#not_trig<br />
#bubka<br />
#AnonAmoz<br />
#davidyko<br />
#toadoncart<br />
#Ars<br />
#bos1234<br />
#Hamster1800<br />
#TheDropOutBoy<br />
#mz94<br />
#rem<br />
#[[User:ProtestanT|ProtestanT]]<br />
#Farrell<br />
#D3m0n Shad0w<br />
#[[User:Azjps|azjps]]<br />
#[[User:Lawrence Wu|Lawrence Wu]]<br />
#miyomiyo<br />
#ZeroFive1<br />
#chessplayingballer<br />
#[[User:CircleSquared|CircleSquared]]<br />
#Rafaelloaa<br />
#nitish<br />
#DonkeyKong<br />
#moogra<br />
#snee<br />
#dbkarp<br />
<br />
===List of Teams===<br />
====Team Alpha (<math>\alpha</math>)====<br />
#i_like_pie - ''<span style="color:blue">Poster</span>''<br />
#7h3.D3m0n.117 - ''<span style="color:blue">Substitute Poster</span>''<br />
#cincodemayo5590<br />
#D3m0n Shad0w<br />
#TheDropOutBoy<br />
<br />
====Team Beta (<math>\beta</math>)====<br />
#Temperal - ''<span style="color:blue">Poster</span>''<br />
#CircleSquared - ''<span style="color:blue">Substitute Poster</span>''<br />
#abacadaea<br />
#miyomiyo<br />
#davidyko<br />
<br />
====Team Gamma (<math>\gamma</math>)====<br />
#nayel - ''<span style="color:blue">Poster</span>''<br />
#BoesFX - ''<span style="color:blue">Substitute Poster</span>''<br />
#mz94<br />
#shaggy75<br />
<br />
====Team Delta (<math>\delta</math>)====<br />
#AnonAmoz - ''<span style="color:blue">Poster</span>''<br />
#nitish - ''<span style="color:blue">Substitute Poster</span>''<br />
#Rafaelloaa<br />
#Lawrence Wu<br />
<br />
====Team Epsilon (<math>\varepsilon</math>)====<br />
#not_trig - ''<span style="color:blue">Poster</span>''<br />
#Hamster1800 - ''<span style="color:blue">Substitute Poster</span>''<br />
#DonkeyKong<br />
#Tenoreoz<br />
<br />
====Team Zeta (<math>\zeta</math>)====<br />
#ProtestanT<br />
#chessplayingballer<br />
#snee<br />
#toadoncart <br />
<br />
====Team Eta (<math>\eta</math>)====<br />
#dbkarp<br />
#rem<br />
#ZeroFive1<br />
#moogra<br />
#Patterns_34<br />
<br />
====Team Theta (<math>\theta</math>)====<br />
#bubka<br />
#Ars<br />
#bos1234<br />
#Farrell<br />
#azjps<br />
<br />
==Rounds==<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 1|Round 1]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 2|Round 2]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 3|Round 3]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 4|Round 4]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Semifinals|Semifinals]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Finals|Finals]]<br />
[[Category: AoPSWiki Games]]</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:Chess/Chess_Tournament_Info&diff=20069AoPS Wiki:Chess/Chess Tournament Info2007-11-24T14:48:24Z<p>7h3.D3m0n.117: /* Team Theta (#\theta$) */</p>
<hr />
<div>__NOTOC__<br />
<br />
:'''Update as of Saturday 11/24: SIGN UPS CLOSED! TOURNAMENT WILL BEGIN SOON!'''<br />
<br />
:'''Note: This article is more updated than the information in the topic; so if there are any discrepancies, then this probably has the correct information!'''<br />
<br />
:'''Note: i_like_pie seems to be currently inactive, so 7h3.D3m0n.117 is temporarily taking over as head TD. Any questions regarding the tournament can be pmed to either Temperal or 7h3.D3m0n.117.'''<br />
<br />
===Teams===<br />
Each team will consist of either 4 or 5 players. It is suggested only people who already know each other make teams of 5 people as it can be harder to communicate with more people. Players can agree between themselves and create their own teams. Others who haven't made their own teams will be randomized into teams.<br />
<br />
During the tournament, a team cannot request to have another player added to their team unless one of their players cannot participate anymore. Players cannot switch teams, so choose wisely if you pick your own teams.<br />
<br />
===Rules===<br />
A team must post a move within 2 days after the other team's move. Each time a team fails to do so (unless there is a good reason), a warning will be issued. 5 warnings will result in disqualification.<br />
<br />
The use of computers, chess programs, and other devices that give your team an advantage is not allowed. This rule cannot be strictly enforced, but hopefully people will play fairly as this tournament is for fun only.<br />
<br />
===Tournament Format===<br />
Depending on the amount of players and teams, there will be several rounds of Swiss, followed by single elimination for the final rounds. For the final game, 3 days will be allowed per move.<br />
<br />
===Signing Up===<br />
Before signing up, please make sure you will be able to participate. [[User:I like pie|I_like_pie]] will accept sign ups via post in the [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=164632 original topic], <url>privmsg.php?mode=post&u=22236 PM</url>, or email (nkouevda@gmail.com).<br />
<br />
Sign ups (as of November 24, 2007) are closed.<br />
<br />
===Playing===<br />
All games will be played on the Math and Strategy forum, with a representative from each team (the designated ''<span style="color:blue">Poster</span>'') posting moves when it is their team's turn. <br />
<br />
All games will be documented on the Wiki:<br />
<br />
Here is the format for the page name of each game: '''AoPSWiki:Chess/Chess Tournament Info/Round <nowiki>#</nowiki>/Game <nowiki>#</nowiki>''', where the first <nowiki>#</nowiki> is the round number and the second is the game number. All of these would be part of '''Category:Current Round # Chess Games'''.<br />
<br />
The format of the last two rounds will be different.<br />
<br />
'''AoPSWiki:Chess/Chess Tournament Info/Semifinals/Game #''': all of these would be part of '''Category:Current Semifinals Chess Games'''<br />
<br />
'''AoPSWiki:Chess/Chess Tournament Info/Finals/Game #''': all of these would be part of '''Category:Current Finals Chess Games'''<br />
===FAQ===<br />
====When will the pairings be up?====<br />
<br />
As mentioned above, pairings will be up in the next week.<br />
----<br />
====When do games start?====<br />
<br />
Games will start in the Math&Strat Forum exactly 7 days after pairings are posted. This allows team members to communicate, get to know each other, and plan their openings. Some people also might be on vacation so this extra week will allow the people to return. An estimated date? December 7.<br />
----<br />
====Do we play the games on Wiki or the Math and Strategy Forum?====<br />
<br />
We would ask you to play the games in the forum because it's easier to keep track of things and it could be confusing for posters on the Wiki. <br />
----<br />
====Will the Wiki game/round pages have any use?====<br />
<br />
Yes, Temperal will be documenting every move on the wiki with those pages to prevent cheating, illegal moves, etc.<br />
----<br />
====Will there be a standardized title for the topics?====<br />
<br />
The titles will be: "Chess tournament: Round x, Game y, Team a vs. Team b".<br />
----<br />
====How many rounds will this tournament be?====<br />
<br />
Four rounds of randomized Swiss, then the semi-finals and finals (referred to collectively as the playoffs), which are single elimination.<br />
----<br />
====Will there be appeals for rematches?====<br />
<br />
No. If you made a terrible mistake unrepresentative of your playing level, so be it. We're not extending this already-long tournament even more.<br />
----<br />
====When will each new round begin?====<br />
<br />
As soon as all games in the previous one are finished. If a game is taking *way* too long, it will be up to a TD's discretion to declare it a win, loss, or draw.<br />
<br />
===List of Players===<br />
35 Players:<br />
#[[User:I like pie|i_like_pie]]<br />
#[[User:7h3.D3m0n.117|7h3.D3m0n.117]]<br />
#cincodemayo5590<br />
#BoesFX<br />
#[[User:Temperal|Temperal]]<br />
#shaggy75<br />
#Tenoreoz<br />
#[[User:abacadaea|abacadaea]]<br />
#[[User:nayel|nayel]]<br />
#not_trig<br />
#bubka<br />
#AnonAmoz<br />
#davidyko<br />
#toadoncart<br />
#Ars<br />
#bos1234<br />
#Hamster1800<br />
#TheDropOutBoy<br />
#mz94<br />
#rem<br />
#[[User:ProtestanT|ProtestanT]]<br />
#Farrell<br />
#D3m0n Shad0w<br />
#[[User:Azjps|azjps]]<br />
#[[User:Lawrence Wu|Lawrence Wu]]<br />
#miyomiyo<br />
#ZeroFive1<br />
#chessplayingballer<br />
#[[User:CircleSquared|CircleSquared]]<br />
#Rafaelloaa<br />
#nitish<br />
#DonkeyKong<br />
#moogra<br />
#snee<br />
#dbkarp<br />
<br />
===List of Teams===<br />
====Team Alpha (<math>\alpha</math>)====<br />
#i_like_pie - ''<span style="color:blue">Poster</span>''<br />
#7h3.D3m0n.117 - ''<span style="color:blue">Substitute Poster</span>''<br />
#cincodemayo5590<br />
#D3m0n Shad0w<br />
#TheDropOutBoy<br />
<br />
====Team Beta (<math>\beta</math>)====<br />
#Temperal - ''<span style="color:blue">Poster</span>''<br />
#CircleSquared - ''<span style="color:blue">Substitute Poster</span>''<br />
#abacadaea<br />
#miyomiyo<br />
#davidyko<br />
<br />
====Team Gamma (<math>\gamma</math>)====<br />
#nayel - ''<span style="color:blue">Poster</span>''<br />
#BoesFX - ''<span style="color:blue">Substitute Poster</span>''<br />
#mz94<br />
#shaggy75<br />
<br />
====Team Delta (<math>\delta</math>)====<br />
#AnonAmoz - ''<span style="color:blue">Poster</span>''<br />
#nitish - ''<span style="color:blue">Substitute Poster</span>''<br />
#Rafaelloaa<br />
#Lawrence Wu<br />
<br />
====Team Epsilon (<math>\varepsilon</math>)====<br />
#not_trig - ''<span style="color:blue">Poster</span>''<br />
#Hamster1800 - ''<span style="color:blue">Substitute Poster</span>''<br />
#DonkeyKong<br />
#Tenoreoz<br />
<br />
====Team Zeta (<math>\zeta</math>)====<br />
#ProtestanT<br />
#chessplayingballer<br />
#snee<br />
#toadoncart <br />
<br />
====Team Eta (<math>\eta</math>)====<br />
#dbkarp<br />
#rem<br />
#ZeroFive1<br />
#moogra<br />
<br />
====Team Theta (<math>\theta</math>)====<br />
#bubka<br />
#Ars<br />
#bos1234<br />
#Farrell<br />
#azjps<br />
<br />
==Rounds==<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 1|Round 1]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 2|Round 2]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 3|Round 3]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 4|Round 4]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Semifinals|Semifinals]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Finals|Finals]]<br />
[[Category: AoPSWiki Games]]</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:Chess/Chess_Tournament_Info&diff=20068AoPS Wiki:Chess/Chess Tournament Info2007-11-24T14:48:14Z<p>7h3.D3m0n.117: /* List of Teams */</p>
<hr />
<div>__NOTOC__<br />
<br />
:'''Update as of Saturday 11/24: SIGN UPS CLOSED! TOURNAMENT WILL BEGIN SOON!'''<br />
<br />
:'''Note: This article is more updated than the information in the topic; so if there are any discrepancies, then this probably has the correct information!'''<br />
<br />
:'''Note: i_like_pie seems to be currently inactive, so 7h3.D3m0n.117 is temporarily taking over as head TD. Any questions regarding the tournament can be pmed to either Temperal or 7h3.D3m0n.117.'''<br />
<br />
===Teams===<br />
Each team will consist of either 4 or 5 players. It is suggested only people who already know each other make teams of 5 people as it can be harder to communicate with more people. Players can agree between themselves and create their own teams. Others who haven't made their own teams will be randomized into teams.<br />
<br />
During the tournament, a team cannot request to have another player added to their team unless one of their players cannot participate anymore. Players cannot switch teams, so choose wisely if you pick your own teams.<br />
<br />
===Rules===<br />
A team must post a move within 2 days after the other team's move. Each time a team fails to do so (unless there is a good reason), a warning will be issued. 5 warnings will result in disqualification.<br />
<br />
The use of computers, chess programs, and other devices that give your team an advantage is not allowed. This rule cannot be strictly enforced, but hopefully people will play fairly as this tournament is for fun only.<br />
<br />
===Tournament Format===<br />
Depending on the amount of players and teams, there will be several rounds of Swiss, followed by single elimination for the final rounds. For the final game, 3 days will be allowed per move.<br />
<br />
===Signing Up===<br />
Before signing up, please make sure you will be able to participate. [[User:I like pie|I_like_pie]] will accept sign ups via post in the [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=164632 original topic], <url>privmsg.php?mode=post&u=22236 PM</url>, or email (nkouevda@gmail.com).<br />
<br />
Sign ups (as of November 24, 2007) are closed.<br />
<br />
===Playing===<br />
All games will be played on the Math and Strategy forum, with a representative from each team (the designated ''<span style="color:blue">Poster</span>'') posting moves when it is their team's turn. <br />
<br />
All games will be documented on the Wiki:<br />
<br />
Here is the format for the page name of each game: '''AoPSWiki:Chess/Chess Tournament Info/Round <nowiki>#</nowiki>/Game <nowiki>#</nowiki>''', where the first <nowiki>#</nowiki> is the round number and the second is the game number. All of these would be part of '''Category:Current Round # Chess Games'''.<br />
<br />
The format of the last two rounds will be different.<br />
<br />
'''AoPSWiki:Chess/Chess Tournament Info/Semifinals/Game #''': all of these would be part of '''Category:Current Semifinals Chess Games'''<br />
<br />
'''AoPSWiki:Chess/Chess Tournament Info/Finals/Game #''': all of these would be part of '''Category:Current Finals Chess Games'''<br />
===FAQ===<br />
====When will the pairings be up?====<br />
<br />
As mentioned above, pairings will be up in the next week.<br />
----<br />
====When do games start?====<br />
<br />
Games will start in the Math&Strat Forum exactly 7 days after pairings are posted. This allows team members to communicate, get to know each other, and plan their openings. Some people also might be on vacation so this extra week will allow the people to return. An estimated date? December 7.<br />
----<br />
====Do we play the games on Wiki or the Math and Strategy Forum?====<br />
<br />
We would ask you to play the games in the forum because it's easier to keep track of things and it could be confusing for posters on the Wiki. <br />
----<br />
====Will the Wiki game/round pages have any use?====<br />
<br />
Yes, Temperal will be documenting every move on the wiki with those pages to prevent cheating, illegal moves, etc.<br />
----<br />
====Will there be a standardized title for the topics?====<br />
<br />
The titles will be: "Chess tournament: Round x, Game y, Team a vs. Team b".<br />
----<br />
====How many rounds will this tournament be?====<br />
<br />
Four rounds of randomized Swiss, then the semi-finals and finals (referred to collectively as the playoffs), which are single elimination.<br />
----<br />
====Will there be appeals for rematches?====<br />
<br />
No. If you made a terrible mistake unrepresentative of your playing level, so be it. We're not extending this already-long tournament even more.<br />
----<br />
====When will each new round begin?====<br />
<br />
As soon as all games in the previous one are finished. If a game is taking *way* too long, it will be up to a TD's discretion to declare it a win, loss, or draw.<br />
<br />
===List of Players===<br />
35 Players:<br />
#[[User:I like pie|i_like_pie]]<br />
#[[User:7h3.D3m0n.117|7h3.D3m0n.117]]<br />
#cincodemayo5590<br />
#BoesFX<br />
#[[User:Temperal|Temperal]]<br />
#shaggy75<br />
#Tenoreoz<br />
#[[User:abacadaea|abacadaea]]<br />
#[[User:nayel|nayel]]<br />
#not_trig<br />
#bubka<br />
#AnonAmoz<br />
#davidyko<br />
#toadoncart<br />
#Ars<br />
#bos1234<br />
#Hamster1800<br />
#TheDropOutBoy<br />
#mz94<br />
#rem<br />
#[[User:ProtestanT|ProtestanT]]<br />
#Farrell<br />
#D3m0n Shad0w<br />
#[[User:Azjps|azjps]]<br />
#[[User:Lawrence Wu|Lawrence Wu]]<br />
#miyomiyo<br />
#ZeroFive1<br />
#chessplayingballer<br />
#[[User:CircleSquared|CircleSquared]]<br />
#Rafaelloaa<br />
#nitish<br />
#DonkeyKong<br />
#moogra<br />
#snee<br />
#dbkarp<br />
<br />
===List of Teams===<br />
====Team Alpha (<math>\alpha</math>)====<br />
#i_like_pie - ''<span style="color:blue">Poster</span>''<br />
#7h3.D3m0n.117 - ''<span style="color:blue">Substitute Poster</span>''<br />
#cincodemayo5590<br />
#D3m0n Shad0w<br />
#TheDropOutBoy<br />
<br />
====Team Beta (<math>\beta</math>)====<br />
#Temperal - ''<span style="color:blue">Poster</span>''<br />
#CircleSquared - ''<span style="color:blue">Substitute Poster</span>''<br />
#abacadaea<br />
#miyomiyo<br />
#davidyko<br />
<br />
====Team Gamma (<math>\gamma</math>)====<br />
#nayel - ''<span style="color:blue">Poster</span>''<br />
#BoesFX - ''<span style="color:blue">Substitute Poster</span>''<br />
#mz94<br />
#shaggy75<br />
<br />
====Team Delta (<math>\delta</math>)====<br />
#AnonAmoz - ''<span style="color:blue">Poster</span>''<br />
#nitish - ''<span style="color:blue">Substitute Poster</span>''<br />
#Rafaelloaa<br />
#Lawrence Wu<br />
<br />
====Team Epsilon (<math>\varepsilon</math>)====<br />
#not_trig - ''<span style="color:blue">Poster</span>''<br />
#Hamster1800 - ''<span style="color:blue">Substitute Poster</span>''<br />
#DonkeyKong<br />
#Tenoreoz<br />
<br />
====Team Zeta (<math>\zeta</math>)====<br />
#ProtestanT<br />
#chessplayingballer<br />
#snee<br />
#toadoncart <br />
<br />
====Team Eta (<math>\eta</math>)====<br />
#dbkarp<br />
#rem<br />
#ZeroFive1<br />
#moogra<br />
<br />
====Team Theta (#\theta$)====<br />
#bubka<br />
#Ars<br />
#bos1234<br />
#Farrell<br />
#azjps<br />
<br />
==Rounds==<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 1|Round 1]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 2|Round 2]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 3|Round 3]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 4|Round 4]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Semifinals|Semifinals]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Finals|Finals]]<br />
[[Category: AoPSWiki Games]]</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:Chess/Chess_Tournament_Info&diff=20067AoPS Wiki:Chess/Chess Tournament Info2007-11-24T14:46:05Z<p>7h3.D3m0n.117: /* Team Epsilon (<math>\varepsilon</math>) */</p>
<hr />
<div>__NOTOC__<br />
<br />
:'''Update as of Saturday 11/24: SIGN UPS CLOSED! TOURNAMENT WILL BEGIN SOON!'''<br />
<br />
:'''Note: This article is more updated than the information in the topic; so if there are any discrepancies, then this probably has the correct information!'''<br />
<br />
:'''Note: i_like_pie seems to be currently inactive, so 7h3.D3m0n.117 is temporarily taking over as head TD. Any questions regarding the tournament can be pmed to either Temperal or 7h3.D3m0n.117.'''<br />
<br />
===Teams===<br />
Each team will consist of either 4 or 5 players. It is suggested only people who already know each other make teams of 5 people as it can be harder to communicate with more people. Players can agree between themselves and create their own teams. Others who haven't made their own teams will be randomized into teams.<br />
<br />
During the tournament, a team cannot request to have another player added to their team unless one of their players cannot participate anymore. Players cannot switch teams, so choose wisely if you pick your own teams.<br />
<br />
===Rules===<br />
A team must post a move within 2 days after the other team's move. Each time a team fails to do so (unless there is a good reason), a warning will be issued. 5 warnings will result in disqualification.<br />
<br />
The use of computers, chess programs, and other devices that give your team an advantage is not allowed. This rule cannot be strictly enforced, but hopefully people will play fairly as this tournament is for fun only.<br />
<br />
===Tournament Format===<br />
Depending on the amount of players and teams, there will be several rounds of Swiss, followed by single elimination for the final rounds. For the final game, 3 days will be allowed per move.<br />
<br />
===Signing Up===<br />
Before signing up, please make sure you will be able to participate. [[User:I like pie|I_like_pie]] will accept sign ups via post in the [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=164632 original topic], <url>privmsg.php?mode=post&u=22236 PM</url>, or email (nkouevda@gmail.com).<br />
<br />
Sign ups (as of November 24, 2007) are closed.<br />
<br />
===Playing===<br />
All games will be played on the Math and Strategy forum, with a representative from each team (the designated ''<span style="color:blue">Poster</span>'') posting moves when it is their team's turn. <br />
<br />
All games will be documented on the Wiki:<br />
<br />
Here is the format for the page name of each game: '''AoPSWiki:Chess/Chess Tournament Info/Round <nowiki>#</nowiki>/Game <nowiki>#</nowiki>''', where the first <nowiki>#</nowiki> is the round number and the second is the game number. All of these would be part of '''Category:Current Round # Chess Games'''.<br />
<br />
The format of the last two rounds will be different.<br />
<br />
'''AoPSWiki:Chess/Chess Tournament Info/Semifinals/Game #''': all of these would be part of '''Category:Current Semifinals Chess Games'''<br />
<br />
'''AoPSWiki:Chess/Chess Tournament Info/Finals/Game #''': all of these would be part of '''Category:Current Finals Chess Games'''<br />
===FAQ===<br />
====When will the pairings be up?====<br />
<br />
As mentioned above, pairings will be up in the next week.<br />
----<br />
====When do games start?====<br />
<br />
Games will start in the Math&Strat Forum exactly 7 days after pairings are posted. This allows team members to communicate, get to know each other, and plan their openings. Some people also might be on vacation so this extra week will allow the people to return. An estimated date? December 7.<br />
----<br />
====Do we play the games on Wiki or the Math and Strategy Forum?====<br />
<br />
We would ask you to play the games in the forum because it's easier to keep track of things and it could be confusing for posters on the Wiki. <br />
----<br />
====Will the Wiki game/round pages have any use?====<br />
<br />
Yes, Temperal will be documenting every move on the wiki with those pages to prevent cheating, illegal moves, etc.<br />
----<br />
====Will there be a standardized title for the topics?====<br />
<br />
The titles will be: "Chess tournament: Round x, Game y, Team a vs. Team b".<br />
----<br />
====How many rounds will this tournament be?====<br />
<br />
Four rounds of randomized Swiss, then the semi-finals and finals (referred to collectively as the playoffs), which are single elimination.<br />
----<br />
====Will there be appeals for rematches?====<br />
<br />
No. If you made a terrible mistake unrepresentative of your playing level, so be it. We're not extending this already-long tournament even more.<br />
----<br />
====When will each new round begin?====<br />
<br />
As soon as all games in the previous one are finished. If a game is taking *way* too long, it will be up to a TD's discretion to declare it a win, loss, or draw.<br />
<br />
===List of Players===<br />
35 Players:<br />
#[[User:I like pie|i_like_pie]]<br />
#[[User:7h3.D3m0n.117|7h3.D3m0n.117]]<br />
#cincodemayo5590<br />
#BoesFX<br />
#[[User:Temperal|Temperal]]<br />
#shaggy75<br />
#Tenoreoz<br />
#[[User:abacadaea|abacadaea]]<br />
#[[User:nayel|nayel]]<br />
#not_trig<br />
#bubka<br />
#AnonAmoz<br />
#davidyko<br />
#toadoncart<br />
#Ars<br />
#bos1234<br />
#Hamster1800<br />
#TheDropOutBoy<br />
#mz94<br />
#rem<br />
#[[User:ProtestanT|ProtestanT]]<br />
#Farrell<br />
#D3m0n Shad0w<br />
#[[User:Azjps|azjps]]<br />
#[[User:Lawrence Wu|Lawrence Wu]]<br />
#miyomiyo<br />
#ZeroFive1<br />
#chessplayingballer<br />
#[[User:CircleSquared|CircleSquared]]<br />
#Rafaelloaa<br />
#nitish<br />
#DonkeyKong<br />
#moogra<br />
#snee<br />
#dbkarp<br />
<br />
===List of Teams===<br />
====Team Alpha (<math>\alpha</math>)====<br />
#i_like_pie - ''<span style="color:blue">Poster</span>''<br />
#7h3.D3m0n.117 - ''<span style="color:blue">Substitute Poster</span>''<br />
#cincodemayo5590<br />
#D3m0n Shad0w<br />
#TheDropOutBoy<br />
<br />
====Team Beta (<math>\beta</math>)====<br />
#Temperal - ''<span style="color:blue">Poster</span>''<br />
#CircleSquared - ''<span style="color:blue">Substitute Poster</span>''<br />
#abacadaea<br />
#miyomiyo<br />
#davidyko<br />
<br />
====Team Gamma (<math>\gamma</math>)====<br />
#nayel - ''<span style="color:blue">Poster</span>''<br />
#BoesFX - ''<span style="color:blue">Substitute Poster</span>''<br />
#mz94<br />
#shaggy75<br />
<br />
====Team Delta (<math>\delta</math>)====<br />
#AnonAmoz - ''<span style="color:blue">Poster</span>''<br />
#nitish - ''<span style="color:blue">Substitute Poster</span>''<br />
#Rafaelloaa<br />
#Lawrence Wu<br />
<br />
====Team Epsilon (<math>\varepsilon</math>)====<br />
#not_trig - ''<span style="color:blue">Poster</span>''<br />
#Hamster1800 - ''<span style="color:blue">Substitute Poster</span>''<br />
#DonkeyKong<br />
#Tenoreoz<br />
<br />
==Rounds==<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 1|Round 1]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 2|Round 2]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 3|Round 3]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 4|Round 4]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Semifinals|Semifinals]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Finals|Finals]]<br />
[[Category: AoPSWiki Games]]</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:Chess/Chess_Tournament_Info&diff=20066AoPS Wiki:Chess/Chess Tournament Info2007-11-24T14:40:31Z<p>7h3.D3m0n.117: /* Signing Up */</p>
<hr />
<div>__NOTOC__<br />
<br />
:'''Update as of Saturday 11/24: SIGN UPS CLOSED! TOURNAMENT WILL BEGIN SOON!'''<br />
<br />
:'''Note: This article is more updated than the information in the topic; so if there are any discrepancies, then this probably has the correct information!'''<br />
<br />
:'''Note: i_like_pie seems to be currently inactive, so 7h3.D3m0n.117 is temporarily taking over as head TD. Any questions regarding the tournament can be pmed to either Temperal or 7h3.D3m0n.117.'''<br />
<br />
===Teams===<br />
Each team will consist of either 4 or 5 players. It is suggested only people who already know each other make teams of 5 people as it can be harder to communicate with more people. Players can agree between themselves and create their own teams. Others who haven't made their own teams will be randomized into teams.<br />
<br />
During the tournament, a team cannot request to have another player added to their team unless one of their players cannot participate anymore. Players cannot switch teams, so choose wisely if you pick your own teams.<br />
<br />
===Rules===<br />
A team must post a move within 2 days after the other team's move. Each time a team fails to do so (unless there is a good reason), a warning will be issued. 5 warnings will result in disqualification.<br />
<br />
The use of computers, chess programs, and other devices that give your team an advantage is not allowed. This rule cannot be strictly enforced, but hopefully people will play fairly as this tournament is for fun only.<br />
<br />
===Tournament Format===<br />
Depending on the amount of players and teams, there will be several rounds of Swiss, followed by single elimination for the final rounds. For the final game, 3 days will be allowed per move.<br />
<br />
===Signing Up===<br />
Before signing up, please make sure you will be able to participate. [[User:I like pie|I_like_pie]] will accept sign ups via post in the [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=164632 original topic], <url>privmsg.php?mode=post&u=22236 PM</url>, or email (nkouevda@gmail.com).<br />
<br />
Sign ups (as of November 24, 2007) are closed.<br />
<br />
===Playing===<br />
All games will be played on the Math and Strategy forum, with a representative from each team (the designated ''<span style="color:blue">Poster</span>'') posting moves when it is their team's turn. <br />
<br />
All games will be documented on the Wiki:<br />
<br />
Here is the format for the page name of each game: '''AoPSWiki:Chess/Chess Tournament Info/Round <nowiki>#</nowiki>/Game <nowiki>#</nowiki>''', where the first <nowiki>#</nowiki> is the round number and the second is the game number. All of these would be part of '''Category:Current Round # Chess Games'''.<br />
<br />
The format of the last two rounds will be different.<br />
<br />
'''AoPSWiki:Chess/Chess Tournament Info/Semifinals/Game #''': all of these would be part of '''Category:Current Semifinals Chess Games'''<br />
<br />
'''AoPSWiki:Chess/Chess Tournament Info/Finals/Game #''': all of these would be part of '''Category:Current Finals Chess Games'''<br />
===FAQ===<br />
====When will the pairings be up?====<br />
<br />
As mentioned above, pairings will be up in the next week.<br />
----<br />
====When do games start?====<br />
<br />
Games will start in the Math&Strat Forum exactly 7 days after pairings are posted. This allows team members to communicate, get to know each other, and plan their openings. Some people also might be on vacation so this extra week will allow the people to return. An estimated date? December 7.<br />
----<br />
====Do we play the games on Wiki or the Math and Strategy Forum?====<br />
<br />
We would ask you to play the games in the forum because it's easier to keep track of things and it could be confusing for posters on the Wiki. <br />
----<br />
====Will the Wiki game/round pages have any use?====<br />
<br />
Yes, Temperal will be documenting every move on the wiki with those pages to prevent cheating, illegal moves, etc.<br />
----<br />
====Will there be a standardized title for the topics?====<br />
<br />
The titles will be: "Chess tournament: Round x, Game y, Team a vs. Team b".<br />
----<br />
====How many rounds will this tournament be?====<br />
<br />
Four rounds of randomized Swiss, then the semi-finals and finals (referred to collectively as the playoffs), which are single elimination.<br />
----<br />
====Will there be appeals for rematches?====<br />
<br />
No. If you made a terrible mistake unrepresentative of your playing level, so be it. We're not extending this already-long tournament even more.<br />
----<br />
====When will each new round begin?====<br />
<br />
As soon as all games in the previous one are finished. If a game is taking *way* too long, it will be up to a TD's discretion to declare it a win, loss, or draw.<br />
<br />
===List of Players===<br />
35 Players:<br />
#[[User:I like pie|i_like_pie]]<br />
#[[User:7h3.D3m0n.117|7h3.D3m0n.117]]<br />
#cincodemayo5590<br />
#BoesFX<br />
#[[User:Temperal|Temperal]]<br />
#shaggy75<br />
#Tenoreoz<br />
#[[User:abacadaea|abacadaea]]<br />
#[[User:nayel|nayel]]<br />
#not_trig<br />
#bubka<br />
#AnonAmoz<br />
#davidyko<br />
#toadoncart<br />
#Ars<br />
#bos1234<br />
#Hamster1800<br />
#TheDropOutBoy<br />
#mz94<br />
#rem<br />
#[[User:ProtestanT|ProtestanT]]<br />
#Farrell<br />
#D3m0n Shad0w<br />
#[[User:Azjps|azjps]]<br />
#[[User:Lawrence Wu|Lawrence Wu]]<br />
#miyomiyo<br />
#ZeroFive1<br />
#chessplayingballer<br />
#[[User:CircleSquared|CircleSquared]]<br />
#Rafaelloaa<br />
#nitish<br />
#DonkeyKong<br />
#moogra<br />
#snee<br />
#dbkarp<br />
<br />
===List of Teams===<br />
====Team Alpha (<math>\alpha</math>)====<br />
#i_like_pie - ''<span style="color:blue">Poster</span>''<br />
#7h3.D3m0n.117 - ''<span style="color:blue">Substitute Poster</span>''<br />
#cincodemayo5590<br />
#D3m0n Shad0w<br />
#TheDropOutBoy<br />
<br />
====Team Beta (<math>\beta</math>)====<br />
#Temperal - ''<span style="color:blue">Poster</span>''<br />
#CircleSquared - ''<span style="color:blue">Substitute Poster</span>''<br />
#abacadaea<br />
#miyomiyo<br />
#davidyko<br />
<br />
====Team Gamma (<math>\gamma</math>)====<br />
#nayel - ''<span style="color:blue">Poster</span>''<br />
#BoesFX - ''<span style="color:blue">Substitute Poster</span>''<br />
#mz94<br />
#shaggy75<br />
<br />
====Team Delta (<math>\delta</math>)====<br />
#AnonAmoz - ''<span style="color:blue">Poster</span>''<br />
#nitish - ''<span style="color:blue">Substitute Poster</span>''<br />
#Rafaelloaa<br />
#Lawrence Wu<br />
<br />
====Team Epsilon (<math>\varepsilon</math>)====<br />
#not_trig - ''<span style="color:blue">Poster</span>''<br />
#Hamster1800 - ''<span style="color:blue">Substitute Poster</span>''<br />
#-- OPEN --<br />
#-- OPEN --<br />
<br />
==Rounds==<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 1|Round 1]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 2|Round 2]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 3|Round 3]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 4|Round 4]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Semifinals|Semifinals]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Finals|Finals]]<br />
[[Category: AoPSWiki Games]]</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:Chess/Chess_Tournament_Info&diff=20065AoPS Wiki:Chess/Chess Tournament Info2007-11-24T14:39:45Z<p>7h3.D3m0n.117: </p>
<hr />
<div>__NOTOC__<br />
<br />
:'''Update as of Saturday 11/24: SIGN UPS CLOSED! TOURNAMENT WILL BEGIN SOON!'''<br />
<br />
:'''Note: This article is more updated than the information in the topic; so if there are any discrepancies, then this probably has the correct information!'''<br />
<br />
:'''Note: i_like_pie seems to be currently inactive, so 7h3.D3m0n.117 is temporarily taking over as head TD. Any questions regarding the tournament can be pmed to either Temperal or 7h3.D3m0n.117.'''<br />
<br />
===Teams===<br />
Each team will consist of either 4 or 5 players. It is suggested only people who already know each other make teams of 5 people as it can be harder to communicate with more people. Players can agree between themselves and create their own teams. Others who haven't made their own teams will be randomized into teams.<br />
<br />
During the tournament, a team cannot request to have another player added to their team unless one of their players cannot participate anymore. Players cannot switch teams, so choose wisely if you pick your own teams.<br />
<br />
===Rules===<br />
A team must post a move within 2 days after the other team's move. Each time a team fails to do so (unless there is a good reason), a warning will be issued. 5 warnings will result in disqualification.<br />
<br />
The use of computers, chess programs, and other devices that give your team an advantage is not allowed. This rule cannot be strictly enforced, but hopefully people will play fairly as this tournament is for fun only.<br />
<br />
===Tournament Format===<br />
Depending on the amount of players and teams, there will be several rounds of Swiss, followed by single elimination for the final rounds. For the final game, 3 days will be allowed per move.<br />
<br />
===Signing Up===<br />
Before signing up, please make sure you will be able to participate. [[User:I like pie|I_like_pie]] will accept sign ups via post in the [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=164632 original topic], <url>privmsg.php?mode=post&u=22236 PM</url>, or email (nkouevda@gmail.com).<br />
<br />
===Playing===<br />
All games will be played on the Math and Strategy forum, with a representative from each team (the designated ''<span style="color:blue">Poster</span>'') posting moves when it is their team's turn. <br />
<br />
All games will be documented on the Wiki:<br />
<br />
Here is the format for the page name of each game: '''AoPSWiki:Chess/Chess Tournament Info/Round <nowiki>#</nowiki>/Game <nowiki>#</nowiki>''', where the first <nowiki>#</nowiki> is the round number and the second is the game number. All of these would be part of '''Category:Current Round # Chess Games'''.<br />
<br />
The format of the last two rounds will be different.<br />
<br />
'''AoPSWiki:Chess/Chess Tournament Info/Semifinals/Game #''': all of these would be part of '''Category:Current Semifinals Chess Games'''<br />
<br />
'''AoPSWiki:Chess/Chess Tournament Info/Finals/Game #''': all of these would be part of '''Category:Current Finals Chess Games'''<br />
===FAQ===<br />
====When will the pairings be up?====<br />
<br />
As mentioned above, pairings will be up in the next week.<br />
----<br />
====When do games start?====<br />
<br />
Games will start in the Math&Strat Forum exactly 7 days after pairings are posted. This allows team members to communicate, get to know each other, and plan their openings. Some people also might be on vacation so this extra week will allow the people to return. An estimated date? December 7.<br />
----<br />
====Do we play the games on Wiki or the Math and Strategy Forum?====<br />
<br />
We would ask you to play the games in the forum because it's easier to keep track of things and it could be confusing for posters on the Wiki. <br />
----<br />
====Will the Wiki game/round pages have any use?====<br />
<br />
Yes, Temperal will be documenting every move on the wiki with those pages to prevent cheating, illegal moves, etc.<br />
----<br />
====Will there be a standardized title for the topics?====<br />
<br />
The titles will be: "Chess tournament: Round x, Game y, Team a vs. Team b".<br />
----<br />
====How many rounds will this tournament be?====<br />
<br />
Four rounds of randomized Swiss, then the semi-finals and finals (referred to collectively as the playoffs), which are single elimination.<br />
----<br />
====Will there be appeals for rematches?====<br />
<br />
No. If you made a terrible mistake unrepresentative of your playing level, so be it. We're not extending this already-long tournament even more.<br />
----<br />
====When will each new round begin?====<br />
<br />
As soon as all games in the previous one are finished. If a game is taking *way* too long, it will be up to a TD's discretion to declare it a win, loss, or draw.<br />
<br />
===List of Players===<br />
35 Players:<br />
#[[User:I like pie|i_like_pie]]<br />
#[[User:7h3.D3m0n.117|7h3.D3m0n.117]]<br />
#cincodemayo5590<br />
#BoesFX<br />
#[[User:Temperal|Temperal]]<br />
#shaggy75<br />
#Tenoreoz<br />
#[[User:abacadaea|abacadaea]]<br />
#[[User:nayel|nayel]]<br />
#not_trig<br />
#bubka<br />
#AnonAmoz<br />
#davidyko<br />
#toadoncart<br />
#Ars<br />
#bos1234<br />
#Hamster1800<br />
#TheDropOutBoy<br />
#mz94<br />
#rem<br />
#[[User:ProtestanT|ProtestanT]]<br />
#Farrell<br />
#D3m0n Shad0w<br />
#[[User:Azjps|azjps]]<br />
#[[User:Lawrence Wu|Lawrence Wu]]<br />
#miyomiyo<br />
#ZeroFive1<br />
#chessplayingballer<br />
#[[User:CircleSquared|CircleSquared]]<br />
#Rafaelloaa<br />
#nitish<br />
#DonkeyKong<br />
#moogra<br />
#snee<br />
#dbkarp<br />
<br />
===List of Teams===<br />
====Team Alpha (<math>\alpha</math>)====<br />
#i_like_pie - ''<span style="color:blue">Poster</span>''<br />
#7h3.D3m0n.117 - ''<span style="color:blue">Substitute Poster</span>''<br />
#cincodemayo5590<br />
#D3m0n Shad0w<br />
#TheDropOutBoy<br />
<br />
====Team Beta (<math>\beta</math>)====<br />
#Temperal - ''<span style="color:blue">Poster</span>''<br />
#CircleSquared - ''<span style="color:blue">Substitute Poster</span>''<br />
#abacadaea<br />
#miyomiyo<br />
#davidyko<br />
<br />
====Team Gamma (<math>\gamma</math>)====<br />
#nayel - ''<span style="color:blue">Poster</span>''<br />
#BoesFX - ''<span style="color:blue">Substitute Poster</span>''<br />
#mz94<br />
#shaggy75<br />
<br />
====Team Delta (<math>\delta</math>)====<br />
#AnonAmoz - ''<span style="color:blue">Poster</span>''<br />
#nitish - ''<span style="color:blue">Substitute Poster</span>''<br />
#Rafaelloaa<br />
#Lawrence Wu<br />
<br />
====Team Epsilon (<math>\varepsilon</math>)====<br />
#not_trig - ''<span style="color:blue">Poster</span>''<br />
#Hamster1800 - ''<span style="color:blue">Substitute Poster</span>''<br />
#-- OPEN --<br />
#-- OPEN --<br />
<br />
==Rounds==<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 1|Round 1]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 2|Round 2]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 3|Round 3]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Round 4|Round 4]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Semifinals|Semifinals]]<br />
*[[AoPSWiki:Chess/Chess Tournament Info/Finals|Finals]]<br />
[[Category: AoPSWiki Games]]</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=Proof_writing&diff=17990Proof writing2007-10-14T01:46:45Z<p>7h3.D3m0n.117: /* Getting Started */</p>
<hr />
<div>{{WotWAnnounce|week=Oct 11-17}}<br />
<br />
'''Proof writing''' is often thought of as one of the most difficult aspects of math education to conquer. However, students who spend time writing about increasingly difficult math topics can develop this skill over time.<br />
<br />
<br />
== Getting Started ==<br />
The fundamental aspects of a good proof are precision, accuracy, and clarity. A single word can change the intended meaning of a proof, so it is best to be as precise as possible. <br />
<br />
There are two different types of proofs: informal and formal.<br />
<br />
A [[formal proof]] is usually in a two-column format. This is favored by many geometry teachers.<br />
<br />
An [[informal proof]] can be in a wide variety of styles. It is usually not as neat as a two-column proof but is far easier to organize. Except in geometry class, the vast majority of proofs worldwide are informal.<br />
<br />
=== Practice ===<br />
[[Art of Problem Solving]] (AoPS) has many resources to help students begin writing proofs. <br />
* The AoPS forums (which you can get to through the '''Community''' tab on the left sidebar) are a great place to practice writing solutions to problems. Do your best to make your explanations both clear and complete. Read solutions by other students to see what you might do better. Listen to the constructive criticisms of others.<br />
* AoPS Blogs (also in the Community area) are a great place to showcase your best solutions.<br />
* The [[AoPSWiki]] you are in now is written by members of the AoPS community. Contributing to the AoPSWiki means writing mathematics as clearly as you can.<br />
<br />
== Proof writing guides ==<br />
* [http://www.artofproblemsolving.com/Resources/AoPS_R_A_HowWrite.php How to Write a Solution] by [[Richard Rusczyk]] and [[Mathew Crawford]]<br />
* [http://www.stonehill.edu/compsci/History_Math/math-read.htm How to Read Mathematics] -- Not really proof writing, but a helpful read for those learning to write basic proofs.<br />
<br />
<br />
== See also ==<br />
* [[Math books]]<br />
* [[Mathematics competitions]]<br />
* [[Mathematics competition resources]]<br />
<br />
{{stub}}</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=Proof_writing&diff=17926Proof writing2007-10-13T01:18:23Z<p>7h3.D3m0n.117: /* Getting Started */</p>
<hr />
<div>{{WotWAnnounce|week=Oct 11-17}}<br />
<br />
'''Proof writing''' is often thought of as one of the most difficult aspects of math education to conquer. However, students who spend time writing about increasingly difficult math topics can develop this skill over time.<br />
<br />
<br />
== Getting Started ==<br />
The fundamental aspects of a good proof are precision, accuracy, and clarity. A single word can change the intended meaning of a proof, so it is best to be as precise as possible. <br />
<br />
There are two different types of proofs: informal and formal.<br />
<br />
A [[formal proof]] is usally in a two-column format. This is favored by many geometry teachers nationwide because of its neatness and clarity.<br />
<br />
An [[informal proof]] can be in a wide variety of styles. It is usually not as neat as a two-column proof but is far easier to organize. Except in geometry class, the vast majority of proofs worldwide are informal.<br />
<br />
=== Practice ===<br />
[[Art of Problem Solving]] (AoPS) has many resources to help students begin writing proofs. <br />
* The AoPS forums (which you can get to through the '''Community''' tab on the left sidebar) are a great place to practice writing solutions to problems. Do your best to make your explanations both clear and complete. Read solutions by other students to see what you might do better. Listen to the constructive criticisms of others.<br />
* AoPS Blogs (also in the Community area) are a great place to showcase your best solutions.<br />
* The [[AoPSWiki]] you are in now is written by members of the AoPS community. Contributing to the AoPSWiki means writing mathematics as clearly as you can.<br />
<br />
== Proof writing guides ==<br />
* [http://www.artofproblemsolving.com/Resources/AoPS_R_A_HowWrite.php How to Write a Solution] by [[Richard Rusczyk]] and [[Mathew Crawford]]<br />
* [http://www.stonehill.edu/compsci/History_Math/math-read.htm How to Read Mathematics] -- Not really proof writing, but a helpful read for those learning to write basic proofs.<br />
<br />
<br />
== See also ==<br />
* [[Math books]]<br />
* [[Mathematics competitions]]<br />
* [[Mathematics competition resources]]<br />
<br />
{{stub}}</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=Proof_writing&diff=17925Proof writing2007-10-13T01:18:00Z<p>7h3.D3m0n.117: /* Getting Started */</p>
<hr />
<div>{{WotWAnnounce|week=Oct 11-17}}<br />
<br />
'''Proof writing''' is often thought of as one of the most difficult aspects of math education to conquer. However, students who spend time writing about increasingly difficult math topics can develop this skill over time.<br />
<br />
<br />
== Getting Started ==<br />
The fundamental aspects of a good proof are precision, accuracy, and clarity. A single word can change the intended meaning of a proof, so it is best to be as precise as possible. <br />
<br />
There are two different types of proofs: informal and formal.<br />
<br />
A formal proof is usally in a two-column format. This is favored by many geometry teachers nationwide because of its neatness and clarity.<br />
<br />
An informal proof can be in a wide variety of styles. It is usually not as neat as a two-column proof but is far easier to organize. Except in geometry class, the vast majority of proofs worldwide are informal.<br />
<br />
=== Practice ===<br />
[[Art of Problem Solving]] (AoPS) has many resources to help students begin writing proofs. <br />
* The AoPS forums (which you can get to through the '''Community''' tab on the left sidebar) are a great place to practice writing solutions to problems. Do your best to make your explanations both clear and complete. Read solutions by other students to see what you might do better. Listen to the constructive criticisms of others.<br />
* AoPS Blogs (also in the Community area) are a great place to showcase your best solutions.<br />
* The [[AoPSWiki]] you are in now is written by members of the AoPS community. Contributing to the AoPSWiki means writing mathematics as clearly as you can.<br />
<br />
== Proof writing guides ==<br />
* [http://www.artofproblemsolving.com/Resources/AoPS_R_A_HowWrite.php How to Write a Solution] by [[Richard Rusczyk]] and [[Mathew Crawford]]<br />
* [http://www.stonehill.edu/compsci/History_Math/math-read.htm How to Read Mathematics] -- Not really proof writing, but a helpful read for those learning to write basic proofs.<br />
<br />
<br />
== See also ==<br />
* [[Math books]]<br />
* [[Mathematics competitions]]<br />
* [[Mathematics competition resources]]<br />
<br />
{{stub}}</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=User:7h3.D3m0n.117&diff=17477User:7h3.D3m0n.1172007-10-07T12:41:16Z<p>7h3.D3m0n.117: </p>
<hr />
<div>[[Image:7h3_D3m0n_117.png]]<br />
<br />
'''AIM''': n0vad3m0n <br><br />
'''E-mail''': khenry117@hotmail.com <br><br />
'''Location''': Maryland <br><br />
'''Blog''': [http://www.artofproblemsolving.com/Forum/weblog.php?w=681]</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=User:7h3.D3m0n.117&diff=17476User:7h3.D3m0n.1172007-10-07T12:40:53Z<p>7h3.D3m0n.117: </p>
<hr />
<div>[[Image:7h3_D3m0n_117.png]]<br />
<br />
'''AIM''': n0vad3m0n <br><br />
'''E-mail''': khenry117@hotmail.com <br><br />
'''Location''': Maryland<br />
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E-mail: khenry117@hotmail.com</div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=Quadratic_formula&diff=16418Quadratic formula2007-09-22T00:37:42Z<p>7h3.D3m0n.117: </p>
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<div>The '''quadratic formula''' is a general [[expression]] for the [[solution]]s to a [[quadratic equation]]. It is used when other methods, such as [[completing the square]], [[factoring]], and [[square root property]] do not work or are too tedious.<br />
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<br />
===General Solution For A Quadratic by Completing the Square===<br />
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Let the quadratic be in the form <math>a\cdot x^2+b\cdot x+c=0</math>. <br />
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Moving ''c'' to the other side, we obtain<br />
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<math>a\cdot x^2+b\cdot x=-c</math><br />
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Dividing by <math>{a}</math> and adding <math>\frac{b^2}{4a^2}</math> to both sides yields<br />
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<math>x^2+\frac{b}{a}x+\frac{b^2}{4a^2}=-\frac{c}{a}+\frac{b^2}{4a^2}</math>.<br />
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Factoring the [[LHS]] gives<br />
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<math>\left(x+\frac{b}{2a}\right)^2=\frac{b^2-4ac}{4a^2}</math><br />
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As described above, an equation in this form can be solved, yielding<br />
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<math>{x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}}</math><br />
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This formula is also called the quadratic formula.<br />
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Given the values <math>{a},{b},{c}</math>, we can find all [[real]] and [[complex number|complex]] solutions to the quadratic equation.<br />
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=== Variation ===<br />
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In some situations, it is preferable to use this variation of the quadratic formula:<br />
<br />
<math>\frac{2c}{-b\pm\sqrt{b^2-4ac}}</math></div>7h3.D3m0n.117https://artofproblemsolving.com/wiki/index.php?title=Euler%27s_number&diff=16417Euler's number2007-09-22T00:35:34Z<p>7h3.D3m0n.117: </p>
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<div>'''e''' is a [[constant]] that appears in a variety of mathematical contexts. It has been shown to be both [[irrational]] and [[transcendental number|transcendental]].<br />
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<math>e=\sum_{n=0}^{\infty} \frac{1}{n!} \approx 2.7182818...</math><br />
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==e and logarithms==<br />
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<math>e</math> can be a base of some [[logarithms]], known as natural logarithms.<br />
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<math>\log_e x = \ln x</math> <br />
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== e and calculus ==<br />
'''e''' is defined as the following [[limit]]: <math>e=\lim_{n\rightarrow \infty}{\left(1+\frac 1n\right)}^n</math>.<br />
In [[calculus]], the fact that <math>e^x = \sum{\frac{x^n}{n!}}</math> is used often, based on the above definition and the [[Binomial Theorem]].<br />
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=== Where <math>e</math> comes from ===<br />
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Suppose <math>b</math> is a positive real number, and <math>f(x) = b^x</math> for all real numbers <math>x</math>. Let's try to figure out what <math>f'(x)</math> is.<br />
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<math>f'(x) = \lim_{\Delta x \to 0} \frac{f(x+\Delta x)-f(x)}{\Delta x} = \lim_{\Delta x \to 0} \frac{b^{x+\Delta x} - b^x}{\Delta x} = \lim_{\Delta x \to 0} b^x \left( \frac {b^{\Delta x} - 1}{\Delta x}\right) = b^x \left(\lim_{\Delta x \to 0} \frac{b^{\Delta x} - 1}{\Delta x}\right)</math>.<br />
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Something special has almost happened. We found the derivative of <math>b^x</math>, and what we got was ''almost'' <math>b^x</math>. In other words, the derivative of this function is ''almost'' the same function that we started with. However, there is that annoying and kind of messy limit on the right that is messing things up.<br />
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It seems like it would be at least cool, if not downright useful, to have a function whose derivative is equal to itself. (In fact, it turns out that such a function is very useful indeed, for example, in finding solutions to certain [[differential equation]]s.) So, let's ask this question: Is it possible to cleverly pick a special value of <math>b</math> in order to make that annoying limit on the right turn out to be equal to <math>1</math>? If this were possible, then for that special value of <math>b</math>, it would in fact be true that the derivative of <math>b^x</math> is just <math>b^x</math>, exactly the same function we started with.<br />
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<br />
Well, the fact is that there is a special value of <math>b</math> which accomplishes this goal. It is approximately <math>2.718</math>, and it is called <math>e</math>. ("<math>e</math>" stands for ''exponential'' and not ''[[Leonhard Euler|Euler]]'', despite the fact that Leonhard Euler was one of the first mathematicians to use it and the one to name it. <math>e</math> is sometimes (perhaps incorrectly) called "Euler's number." However, [[Napier]] came close to discovering <math>e</math> (or, rather, <math>1/e</math>) before Euler did.)<br />
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So, how do we choose <math>b</math> so that <math>\lim_{\Delta x \to 0} \frac{b^{\Delta x} - 1}{\Delta x} = 1</math>? Could we pick <math>b</math> in some clever way to make this expression simplify? As a first rough idea, imagine what would happen to the expression <math>\frac{b^{\Delta x}-1}{\Delta x}</math> if <math>b</math> were equal to <math>(1+\Delta x)^{\frac{1}{\Delta x} }</math>. Everything cancels out nicely, and we are left with just <math>1</math>. This suggests that we should select <math>b</math> to be <math>\lim_{\Delta x \to 0} (1+\Delta x)^{\frac{1}{\Delta x}}</math>. Here we have our definition of <math>e</math>. This limit is approximately <math>2.718</math>.<br />
<br />
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To make this rigorous, it should be possible to prove that this limit actually exists. Once we define <math>e</math> to be this limit, it should be possible to prove that <math>\lim_{\Delta x \to 0} \frac{e^{\Delta x}-1}{\Delta x} = 1</math>.<br />
<br />
<br />
(This definition of <math>e</math> is equivalent to the one given at the beginning of this article. Just let <math>M = \frac{1}{\Delta x}</math>. Then <math>\lim_{\Delta x \to 0} (1+\Delta x)^{\frac{1}{\Delta x}} = \lim_{M \to \infty} \left(1 + \frac{1}{M}\right)^M</math>.)<br />
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== See also ==<br />
* [[Exponents]]<br />
* [[Algebra]]<br />
* [[Logarithms]]<br />
* [[Calculus]]<br />
* [[Exponential form]]<br />
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[[Category:Constants]]</div>7h3.D3m0n.117